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variants of this functions
Hypergeometric2F1






Mathematica Notation

Traditional Notation









Hypergeometric Functions > Hypergeometric2F1[a,b,c,z] > Specific values > For rational parameters with denominators 4 and fixed z > For fixed z and a=1, b>=a > For fixed z and a=1, b=4





http://functions.wolfram.com/07.23.03.ajhx.01









  


  










Input Form





Hypergeometric2F1[1, 4, -(23/4), z] == (1/4922368) ((1/(-1 + z)^10) (8 (615296 - 6580992 z + 32419200 z^2 - 98323456 z^3 + 209895168 z^4 - 358187520 z^5 + 685326080 z^6 + 162885195 z^7 - 19208772 z^8 + 1384416 z^9)) - (3661347690 Sqrt[2] z^(27/4) ArcTan[1 - z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))])/(1 - z)^(43/4) - (3661347690 Sqrt[2] z^(27/4) ArcTan[1 + z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))])/(1 - z)^(43/4) - (1830673845 Sqrt[2] z^(27/4) Log[1 - (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[z]/Sqrt[1 - z]])/(1 - z)^(43/4) + (1830673845 Sqrt[2] z^(27/4) Log[1 + (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[z]/Sqrt[1 - z]])/(1 - z)^(43/4))










Standard Form





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MathML Form







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Rule Form





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Date Added to functions.wolfram.com (modification date)





2007-05-02